Local oxygen gradients near isolated mitochondria

The oxygen concentration in tissue can vary on several length scales. The basic scale of variation is determined by capillary spacing. It is this scale that is manifest in the simplest Krogh cylinder model. A second, smaller scale of variation is associated with the consumption of oxygen by mitochondria. This paper gives a theoretical analysis of these smaller-scale oxygen variations near an isolated mitochondrion. To illustrate the effects of shape, we have carried out the calculations for prolate spheroids as well as for spheres. The principal result is that the local drop in oxygen pressure around a consuming mitochondrion is of the order of (gamma/3K) (3V/4 pi)2/3, where gamma is the oxygen consumption rate per unit mitochondrial volume, K is the Krogh oxygen diffusivity of the surrounding tissue, and V is the mitochondrial volume. The theory is applied to skeletal muscle in vivo and to hepatocytes in cell suspension experiments. In both cases, we find that local oxygen variations produced by oxygen consumption are much smaller than the cell-wide variations produced by the collective effect of all the mitochondria. For example, in maximally consuming skeletal muscle, the drop in oxygen pressure around a consuming mitochondrion is only of the order of 0.03 Torr.